This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present disclosure. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the disclosed methodologies and techniques. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Hydrocarbon prospecting typically involves obtaining measurements of the subsurface and forming a subsurface model from the measurements. The subsurface model, which may be referred to as a static reservoir model, provides the various structures present in the subsurface formation. Then, the static reservoir model is used to create a dynamic reservoir model by upscaling the static reservoir model into another model scale. As part of this process, the creation of the static reservoir model may include building a structural framework using faults and stratigraphic horizons, constructing a cellular grid based on the structural framework, and filling the cellular grid with subsurface parameters for use in fluid flow simulation.
Within the field of reservoir modeling, geostatistical simulation is the conventional method for populating the cellular grid with subsurface parameters. As an example, Haldorsen describes various stochastic modeling methods as applies to reservoir modeling. See, e.g., Haldorsen, H. Damsleth, E., 1990, “Stochastic Modeling”, Society of Petroleum Engineers, Journal of Petroleum Technology, Volume 42, Number 4, p. 404-412, SPE 21255 and 21299. The reference describes that geostatistical simulation provides a more realistic representation of geology than spatial interpolation. The reference further describes that these stochastic models are then used for fluid flow simulations for reservoir performance prediction estimates.
Furthering this technique, geostatistical methods have extended the point-to-point simulation to multiple-point simulation techniques. As an example, the Strebelle reference describes borrowing the required multiple-point statistics from training images depicting the expected patterns of geological heterogeneities. See, e.g., Strebelle, S., 2002, “Conditional Simulation of Complex Geologic Structures Using Multiple Point Statistics”, Mathematical Geology, January 2002, Volume 34, Issue 1, pp 1-21, 2002). The reference further describes that the methods are tested on the simulation of a fluvial hydrocarbon reservoir with meandering channels.
As another example, the Galli reference describes the use of multiple Gaussian random fields called plurigaussian simulation. See, e.g., Galli, A., Beucher, H., 1997, “Stochastic models for reservoir characterization: a user-friendly review”, Latin American and Caribbean Petroleum Engineering Conference, 30 Aug.-3 Sep. 1997, Rio de Janeiro, Brazil, SPE 38999. This reference describes various types of stochastic models that are conventionally utilized. While plurigaussian simulation is used to preserve spatial continuity and juxtaposition of discrete indicators, it is difficult to parameterize and still relies on sequential simulation within a predefined cellular grid.
As yet another example, the Yarus reference describes sampling uncertainty by producing several possible 3D geological realizations instead of one best and probably flawed—deterministic model. See, e.g., Yarus, J., Chambers, R. L., 2006, “Practical Geostatistics—An Armchair Overview for Petroleum Reservoir Engineers”, Journal of Petroleum Technology, Volume 58, Number 11, p. 78-86, SPE 103357. The reference describes that geostatistical simulation is a sequential method, which the cells of a grid are simulated in a random order. See id. Therefore each random path through the cellular grid yields an equally valid but different result. Many realizations of these stochastic models are necessary to capture the uncertainty in the stochastic parameterization. This sequential simulation paradigm leaves little room for optimization of the algorithms, necessitates many realizations and consequently takes a long time.
The methods described in these different references, each use a nested parameter population strategy. That is, the methods start by populating the cellular grid with an indicator or a discrete property, such as facies or rock type. Then, a continuous petrophysical property, such as porosity or grain size is populated with potentially different algorithmic parameters within each indicator or discrete domain. The nesting of the population is a workflow technique to handle the change in statistical distribution of the continuous properties based on a blocking indicator variable like facies or rock type. The basis for this approach is that the discrete properties may be more spatially predictive over a larger scale that the continuous property. As a result, a modeler can populate the semblance of non-stationarity of the final petrophysical property. Also, the modeler may model continuity of the discrete property separately from the continuous property, potentially at different continuity scales.
However, these techniques have certain limitations. For example, as models utilized in fluid flow simulators are larger and the resolution is finer (e.g., smaller cell size), the computational time for the above methods increases and is computationally inefficient. The inefficiency is a result of the sequential nature of the simulation methods along with the number of cells used in the reservoir model. This fact is further compounded by the typical method of applying a nested approach to modeling wherein two methods of geostatistical simulation are applied in sequence. As such, fluid flow simulations that utilize the conventional parallel processing approach are bottlenecked by the parameter population in the reservoir modeling workflow.
As a result, an enhancement to parameter population techniques is needed to efficiently model hydrocarbon reservoirs for fluid flow simulation. Some of the results of the fluid flow simulation may be feedback into the workflow to adjust certain parameters of the parameter population.